An almost periodic function in the mean

Square-mean Almost Periodic Solutions Nonautonomous Stochastic Differential Equations

This paper concerns the square-mean almost periodic solutions to a class of nonautonomous stochastic differential equations on a separable real Hilbert space. Using the so-called ‘Acquistapace-Terreni’ conditions, we establish the existence and uniqueness of a square-mean almost periodic mild solution to those nonautonomous stochastic differential equations.

An Almost Periodic Noncommutative Wiener’s Lemma

We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.

Characterization of almost maximally almost-periodic groups

Let G be an abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n(G, τ) of (G, τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n(n(G)) 6= n(G) if and only if n(G) is not dually embedded. In particular, n(n(Z, τ)) = n(Z, τ) for any Hausdorff group topology τ on Z. We shall write our a...

Almost Periodic Harmonizable Processes

The class of harmonizable processes is a natural extension of the class of stationary processes. This paper provides sufficient conditions for the sample paths of harmonizable processes to be almost periodic uniformly, Stepanov and Besicovitch.

Almost Periodic Compactifications